A theoretical study on the multi-channel hydrogen addition of maleimide containing 2-hydroxy-benzophenone onto polyethylene in ultra-violet (UV) radiation cross-linking process was carried out using density functional theory (DFT) method at the B3LYP/6-311 + G(d,p) level. The energetic information and the minimum energy path (MEP) are calculated for nine reaction channels. The electrophilic addition reactions at two positions in the target molecule (maleimide containing 2-hydroxy-benzophenone) were investigated, which are on the C atom of C = C groups and on the O atom of C = O groups. Frontier molecular orbitals (MOs) and natural bond orbital (NBO) charge population of the target molecule have been analyzed in detail. As a result, the reaction site of C in C = C group is more active than the site of O in C = O groups. The target molecule can be used as a multi-functional additive candidate. The predicted mechanism may provide a theoretical basis for the real application of cross-linked polyethylene (XLPE) high-voltage insulation cables.